A pilot starting from Athens, New York, wishes to fly to Sparta, New York, which is 320 km from Athens in the direction 20.0° N of E. The pilot heads directly for Sparta and flies at an airspeed of 160 km/h. After flying for 2.0 h, the pilot expects to be at Sparta, but instead he finds himself 20 km due west of Sparta. He has forgotten to correct for the wind.
(a) What is the velocity of the plane relative to the air?
(b) Find the velocity (magnitude and direction) of the plane relative to the ground.
(c) Find the wind speed and direction.